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# Four positive integers $p,q,r,s$ satisfy the following equations:

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Four positive integers $p,q,r,s$ satisfy the following equations:

\begin{align*} pq+2p+q&=348 \\ qr+4q+3r&=373 \\ rs+8r+6s&=544 \end{align*}

What are $p,q,r,$ and $s$?

Nov 5, 2020

#1
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By computer program p = 34, q = 8, r = 16, and s = 27.

Nov 5, 2020
#2
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a=0;p=0; b=0;c=0;d=0;n=a*b+2*a+b;m=b*c+4*b+3*c;l=c*d+8*c+6*d;if(n==348 and m==373 and l==544, goto loop, goto next);loop:p=p+1;printp," =",a,b,c,d;next:a++;if(a<50, goto5,0);a=0;b++;if(b<50, goto5, 0);a=0;b=0;c++;if(c<50, goto5,0);a=0;b=0;c=0;d++;if(d<50, goto5, discard=0;printp

p = 34, q = 8, r = 31, s = 8

Nov 5, 2020
#3
+1

See algebraic solution #2 here:  https://web2.0calc.com/questions/how-do-i-solve-this_22

Guest Nov 5, 2020
#4
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Thanks guests and Alan

Melody  Nov 5, 2020